1. Field of the Invention
This invention relates to tuners for proportional-integral-derivative (PID) controllers in process control systems.
2. Prior Art
The literature is replete with techniques and discussions of how to tune the controller in a process control system to optimize process performance. One of the classic discussions on this subject is an article by Ziegler and Nichols in the transaction of the American Society of Mechanical Engineers Vol. 64, Nov. 1942, at P. 759. Fundamentally, these systems rely on applying a step function to the system and measuring the change at the output from the system as a function of time. The curve thus derived consists of a dead time plus a simple, or compound exponential curve. If multiple capacitances exist in the system (as is generally the case) an "S" shaped curve is obtained, with an initial dead time representing the inertia of the system. It has been customary to derive a time constant (representing the transfer function of the plant or process) by drawing a line tangent to the response curve at its point of inflection and determining the slope (R) of that line and its point of intersection with the time axis. The length of time (L) between the commencement of the response curve and the intersection of the tangent line with the time axis could also be easily determined. It was called the "lag" of the system by Ziegler and Nichols and they taught that the best setting for the proportional action factor (K.sub.1) could be obtained when: EQU K.sub.1 =P/RL
where P is the process change to be corrected.
Derivative and integral action settings can also be found from the process reaction curve using the slope of the tangent to the point of inflection. However, this method is not accurate for several reasons. First, the point of inflection may be indistinct and the slope of the tangent line may, therefore, be inaccurately determined. The result is an erroneous controller setting. Fundamentally, the resolution and accuracy of the prior art systems were low and subject to various human factors which further reduced their accuracy.
In addition, the application of a step function to a process results in a long-term disturbance of the process which makes the use of the step function approach unattractive to the production personnel of the factory incorporating the process.